Decentralized and Dynamic Bandwidth Allocation ... - Semantic Scholar
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems Ahmad T. Al-Hammouri, Michael S. Branicky, Vincenzo Liberatore Case Western Reserve University Stephen M. Phillips Arizona State University April 25, 2006 Support by: NSF CCR-0329910, Department of Commerce TOP 39-6004003, NASA NNC04AA12A, and an OhioICE Training grant
Paper Overview Control over Networks NCSs, DCSs, SANETs, …
Control of Networks Efficient BW allocation Congestion control
Fairness
We propose a “Cof N” scheme to better serve “Cover N” Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
2/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
3/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
4/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
5/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
6/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
7/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
8/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
9/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
10/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
11/45
Control over Networks Remote interaction (monitoring & control) with the physical world Applications:
Industrial automation & process control Space exploration, e.g., telerobotics Smart homes Medical sensing & surgical simulations Automatic asset mgmt. (RFID) Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
12/45
Control of Networks (Scope of the paper) A bandwidth allocation scheme Objectives:
Stability of control systems Efficiency & fairness Fully distributed, asynchronous, & scalable Dynamic & self reconfigurable
Formulating the scheme in CT NCSs regulate h based on congestion fed back from the network Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
13/45
Sampling Rate & Network Congestion h=1/r
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
14/45
Sampling Rate & Network Congestion
l1
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
l2
15/45
Problem Formulation Define a utility fn U(r) that is Monotonically increasing Strictly concave Defined for r ≥ rmin
Optimization formulation max ∑ i Ui (ri ) s.t.
∑
i∈S ( l )
ri ≤ Cl , l = 1,..., L
and ri ≥ r min, i Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
16/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
17/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
18/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
19/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
20/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
21/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
22/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
23/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
NCS Controller
Router p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
24/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
25/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
26/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
r ( pt ) = 1 h = ⎡⎣U ' ( pt ) ⎤⎦ −1
Ahmad Al-Hammouri
r max r min
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
27/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
28/45
NCS-AQM Control Loop
NCS Plant
Queue
r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
29/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Queue tf
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
30/45
NCS-AQM Control Loop
NCS Plant −1
r ( p) = U ' ( p)
Ahmad Al-Hammouri
Queue tf
q`=Σr(t) - C
q(t)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
31/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Queue tf
q`=Σr(t) - C
q(t)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
p(t) f(q(t))
32/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Queue tf
q`=Σr(t) - C
q(t)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
p(t) f(q(t))
33/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Queue tf
q`=Σr(t) - C
q(t)
p(t) f(q(t))
tb
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
34/45
NCS-AQM Control Loop
NCS Plant
Model Plant q`=Σr(t) - C r ( p) = U ' ( p) t B − sd P(s) = s e −1
Queue q(t)
f
p(t) f(q(t))
tb
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
35/45
NCS-AQM Control Loop
NCS Plant
Model Plant q`=Σr(t) - C r ( p) = U ' ( p) t B − sd P(s) = s e −1
f
Queue q(t)
Queue p(t) f(q(t)) Controller G(s)
tb
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
36/45
Queue Controller G(s) Proportional (P) Controller GP(s) = kp
Proportional-Integral (PI) Controller GPI(s) = kp + ki/s q0 +
Ahmad Al-Hammouri
e _
G(s)
u
q(s) P(s)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
37/45
Determination of kp and ki Stability region in the ki–kp plane Stabilizes the NCS-AQM closed-loop system for delays less or equal d
Analysis of quasi-polynomials, f(s,es)
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
38/45
u (tj ) = − K ( R − x(tj ))
Simulations & Results 50 NCS Plants: dx = ax(t ) + bu (t ) dt a − bK a / r • U (r ) = e a
•
a • r min = ln bK + a bK − a [Branicky et al. 2002] [Zhang et al. 2001]
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
39/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
40/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
41/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
42/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
43/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
44/45
Thank You Questions Comments Probing further: http://start.case.edu/~vxl11/NetBots
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
45/45
Paper Overview Control over Networks NCSs, DCSs, SANETs, …
Control of Networks Efficient BW allocation Congestion control
Fairness
We propose a “Cof N” scheme to better serve “Cover N” Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
2/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
3/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
4/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
5/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
6/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
7/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
8/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
9/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
10/45
Control over Networks
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
11/45
Control over Networks Remote interaction (monitoring & control) with the physical world Applications:
Industrial automation & process control Space exploration, e.g., telerobotics Smart homes Medical sensing & surgical simulations Automatic asset mgmt. (RFID) Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
12/45
Control of Networks (Scope of the paper) A bandwidth allocation scheme Objectives:
Stability of control systems Efficiency & fairness Fully distributed, asynchronous, & scalable Dynamic & self reconfigurable
Formulating the scheme in CT NCSs regulate h based on congestion fed back from the network Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
13/45
Sampling Rate & Network Congestion h=1/r
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
14/45
Sampling Rate & Network Congestion
l1
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
l2
15/45
Problem Formulation Define a utility fn U(r) that is Monotonically increasing Strictly concave Defined for r ≥ rmin
Optimization formulation max ∑ i Ui (ri ) s.t.
∑
i∈S ( l )
ri ≤ Cl , l = 1,..., L
and ri ≥ r min, i Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
16/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
17/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
18/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
19/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
20/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
21/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
22/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
23/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
NCS Controller
Router p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
24/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
25/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
26/45
Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS Plant
Router
NCS Controller
p
r ( pt ) = 1 h = ⎡⎣U ' ( pt ) ⎤⎦ −1
Ahmad Al-Hammouri
r max r min
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
27/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
28/45
NCS-AQM Control Loop
NCS Plant
Queue
r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
29/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Queue tf
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
30/45
NCS-AQM Control Loop
NCS Plant −1
r ( p) = U ' ( p)
Ahmad Al-Hammouri
Queue tf
q`=Σr(t) - C
q(t)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
31/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Queue tf
q`=Σr(t) - C
q(t)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
p(t) f(q(t))
32/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Ahmad Al-Hammouri
Queue tf
q`=Σr(t) - C
q(t)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
p(t) f(q(t))
33/45
NCS-AQM Control Loop
NCS Plant r ( p ) = U '−1 ( p)
Queue tf
q`=Σr(t) - C
q(t)
p(t) f(q(t))
tb
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
34/45
NCS-AQM Control Loop
NCS Plant
Model Plant q`=Σr(t) - C r ( p) = U ' ( p) t B − sd P(s) = s e −1
Queue q(t)
f
p(t) f(q(t))
tb
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
35/45
NCS-AQM Control Loop
NCS Plant
Model Plant q`=Σr(t) - C r ( p) = U ' ( p) t B − sd P(s) = s e −1
f
Queue q(t)
Queue p(t) f(q(t)) Controller G(s)
tb
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
36/45
Queue Controller G(s) Proportional (P) Controller GP(s) = kp
Proportional-Integral (PI) Controller GPI(s) = kp + ki/s q0 +
Ahmad Al-Hammouri
e _
G(s)
u
q(s) P(s)
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
37/45
Determination of kp and ki Stability region in the ki–kp plane Stabilizes the NCS-AQM closed-loop system for delays less or equal d
Analysis of quasi-polynomials, f(s,es)
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
38/45
u (tj ) = − K ( R − x(tj ))
Simulations & Results 50 NCS Plants: dx = ax(t ) + bu (t ) dt a − bK a / r • U (r ) = e a
•
a • r min = ln bK + a bK − a [Branicky et al. 2002] [Zhang et al. 2001]
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
39/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
40/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
41/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
42/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
43/45
Simulations & Results (cont.)
PI ¤ P ¤
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
44/45
Thank You Questions Comments Probing further: http://start.case.edu/~vxl11/NetBots
Ahmad Al-Hammouri
Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06)
45/45
